Good sequencings for small Mendelsohn triple systems

• Published in: arXiv.org
• Main Authors: Kreher, Donald L, Stinson, Douglas R, Veitch, Shannon
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.09.2019
• Subjects: Graph theory; Permutations
• ISSN: 2331-8422

A Mendelsohn triple system of order \(v\) (or MTS\((v)\)) is a decomposition of the complete graph into directed 3-cyles. We denote the directed 3-cycle with edges \((x,y)\), \((y,z)\) and \((z,x)\) by \((x,y,z)\), \((y,z,x)\) or \((z,x,y)\). An \(\ell\)-good sequencing of a MTS\((v)\) is a permutation of the points of the design, say \([x_1 \; \cdots \; x_v]\), such that, for every triple \((x,y,z)\) in the design, it is not the case that \(x = x_i\), \(y = x_j\) and \(z = x_k\) with \(i < j < k\) and \(k-i+1 \leq \ell\); or with \(j < k < i\) and \(i-j+1 \leq \ell\); or with \(k < i < j\) and \(j-k+1 \leq \ell\).